`∀[T:Type]. ∀[L:T List]. ∀[P:T ⟶ 𝔹].  uiff(remove_leading(x.P[x];L) = [] ∈ (T List);(∀x∈L.↑P[x]))`

Proof

Definitions occuring in Statement :  remove_leading: `remove_leading(a.P[a];L)` l_all: `(∀x∈L.P[x])` nil: `[]` list: `T List` assert: `↑b` bool: `𝔹` uiff: `uiff(P;Q)` uall: `∀[x:A]. B[x]` so_apply: `x[s]` function: `x:A ⟶ B[x]` universe: `Type` equal: `s = t ∈ T`
Definitions unfolded in proof :  uiff: `uiff(P;Q)` and: `P ∧ Q` uimplies: `b supposing a` member: `t ∈ T` prop: `ℙ` uall: `∀[x:A]. B[x]` so_lambda: `λ2x.t[x]` so_apply: `x[s]` subtype_rel: `A ⊆r B` guard: `{T}` top: `Top` implies: `P `` Q` int_seg: `{i..j-}` lelt: `i ≤ j < k` all: `∀x:A. B[x]` decidable: `Dec(P)` or: `P ∨ Q` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` false: `False` not: `¬A` less_than: `a < b` squash: `↓T` l_all: `(∀x∈L.P[x])` rev_implies: `P `` Q` iff: `P `⇐⇒` Q`
Lemmas referenced :  equal-wf-T-base list_wf remove_leading_wf assert_wf null_wf3 subtype_rel_list top_wf subtype_rel_set not_wf hd_wf uiff_wf l_all_wf2 l_member_wf select_wf int_seg_properties length_wf decidable__le satisfiable-full-omega-tt intformand_wf intformnot_wf intformle_wf itermConstant_wf itermVar_wf int_formula_prop_and_lemma int_formula_prop_not_lemma int_formula_prop_le_lemma int_term_value_constant_lemma int_term_value_var_lemma int_formula_prop_wf decidable__lt intformless_wf int_formula_prop_less_lemma int_seg_wf bool_wf assert_witness iff_weakening_uiff assert_of_null null_remove_leading
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity independent_pairFormation isect_memberFormation hypothesis cut introduction extract_by_obid sqequalHypSubstitution isectElimination thin cumulativity hypothesisEquality sqequalRule lambdaEquality applyEquality functionExtensionality because_Cache baseClosed equalityTransitivity equalitySymmetry independent_isectElimination isect_memberEquality voidElimination voidEquality instantiate functionEquality universeEquality setElimination rename setEquality natural_numberEquality productElimination dependent_functionElimination unionElimination dependent_pairFormation int_eqEquality intEquality computeAll imageElimination independent_pairEquality independent_functionElimination axiomEquality addLevel

Latex:
\mforall{}[T:Type].  \mforall{}[L:T  List].  \mforall{}[P:T  {}\mrightarrow{}  \mBbbB{}].    uiff(remove\_leading(x.P[x];L)  =  [];(\mforall{}x\mmember{}L.\muparrow{}P[x]))

Date html generated: 2018_05_21-PM-06_44_16
Last ObjectModification: 2017_07_26-PM-04_54_56

Theory : general

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