Nuprl Lemma : is-list-map

`∀[t,f:Top].  (is-list(map(f;t)) ~ is-list(t))`

Proof

Definitions occuring in Statement :  is-list: `is-list(t)` map: `map(f;as)` uall: `∀[x:A]. B[x]` top: `Top` sqequal: `s ~ t`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` all: `∀x:A. B[x]` map: `map(f;as)` list_ind: list_ind nat: `ℕ` implies: `P `` Q` false: `False` ge: `i ≥ j ` uimplies: `b supposing a` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` not: `¬A` top: `Top` and: `P ∧ Q` prop: `ℙ` is-list: `is-list(t)` pi2: `snd(t)` btrue: `tt` it: `⋅` fun_exp: `f^n` primrec: `primrec(n;b;c)` so_lambda: `λ2x.t[x]` so_apply: `x[s]` decidable: `Dec(P)` or: `P ∨ Q` nat_plus: `ℕ+` so_lambda: `so_lambda(x,y,z,w.t[x; y; z; w])` so_apply: `x[s1;s2;s3;s4]` strict4: `strict4(F)` has-value: `(a)↓` guard: `{T}` squash: `↓T` subtype_rel: `A ⊆r B` cons: `[a / b]` nil: `[]`
Lemmas referenced :  nat_properties satisfiable-full-omega-tt intformand_wf intformle_wf itermConstant_wf itermVar_wf intformless_wf int_formula_prop_and_lemma int_formula_prop_le_lemma int_term_value_constant_lemma int_term_value_var_lemma int_formula_prop_less_lemma int_formula_prop_wf ge_wf less_than_wf base_wf strictness-apply strictness-callbyvalue bottom-sqle decidable__le subtract_wf intformnot_wf itermSubtract_wf int_formula_prop_not_lemma int_term_value_subtract_lemma fun_exp_unroll_1 top_wf lifting-strict-callbyvalue has-value_wf_base is-exception_wf cbv_sqle int_subtype_base has-value-implies-dec-ispair-2 has-value-implies-dec-isaxiom-2 cbv_bottom_lemma
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalRule thin sqequalSqle lambdaFormation fixpointLeast extract_by_obid sqequalHypSubstitution isectElimination hypothesisEquality hypothesis setElimination rename intWeakElimination natural_numberEquality independent_isectElimination dependent_pairFormation lambdaEquality int_eqEquality intEquality dependent_functionElimination isect_memberEquality voidElimination voidEquality independent_pairFormation computeAll independent_functionElimination axiomSqleEquality unionElimination dependent_set_memberEquality because_Cache sqequalAxiom baseClosed callbyvalueCallbyvalue callbyvalueReduce baseApply closedConclusion callbyvalueExceptionCases inrFormation imageMemberEquality imageElimination exceptionSqequal inlFormation instantiate applyEquality sqleReflexivity divergentSqle

Latex:
\mforall{}[t,f:Top].    (is-list(map(f;t))  \msim{}  is-list(t))

Date html generated: 2018_05_21-PM-10_18_53
Last ObjectModification: 2017_02_27-PM-02_08_08

Theory : eval!all

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