Nuprl Lemma : weak-continuity-bool-bool

`weak-continuity(𝔹;𝔹)`

Proof

Definitions occuring in Statement :  weak-continuity: `weak-continuity(T;V)` bool: `𝔹`
Definitions unfolded in proof :  weak-continuity: `weak-continuity(T;V)` all: `∀x:A. B[x]` member: `t ∈ T` squash: `↓T` exists: `∃x:A. B[x]` implies: `P `` Q` uall: `∀[x:A]. B[x]` subtype_rel: `A ⊆r B` nat: `ℕ` uimplies: `b supposing a` le: `A ≤ B` and: `P ∧ Q` less_than': `less_than'(a;b)` false: `False` not: `¬A` true: `True` prop: `ℙ` cand: `A c∧ B` quotient: `x,y:A//B[x; y]` int_seg: `{i..j-}` lelt: `i ≤ j < k` less_than: `a < b` decidable: `Dec(P)` or: `P ∨ Q` satisfiable_int_formula: `satisfiable_int_formula(fmla)` guard: `{T}` iff: `P `⇐⇒` Q` rev_implies: `P `` Q`
Lemmas referenced :  strong-continuity2-implies-weak-skolem-cantor istype-nat bool_wf int_seg_wf subtype_rel_function nat_wf int_seg_subtype_nat istype-false subtype_rel_self istype-true squash_wf equal_wf member_wf true_wf istype-universe int_seg_properties decidable__le full-omega-unsat intformand_wf intformnot_wf intformle_wf itermConstant_wf itermVar_wf istype-int 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 istype-le iff_weakening_equal
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity lambdaFormation_alt cut introduction extract_by_obid sqequalHypSubstitution dependent_functionElimination thin hypothesisEquality hypothesis imageElimination sqequalRule imageMemberEquality baseClosed functionIsType universeIsType productIsType inhabitedIsType because_Cache equalityIstype isectElimination natural_numberEquality applyEquality lambdaEquality_alt setElimination rename independent_isectElimination independent_pairFormation promote_hyp productEquality functionEquality pointwiseFunctionality pertypeElimination productElimination independent_functionElimination sqequalBase equalitySymmetry equalityTransitivity dependent_pairFormation_alt functionExtensionality_alt instantiate universeEquality dependent_set_memberEquality_alt unionElimination approximateComputation int_eqEquality Error :memTop,  voidElimination

Latex:
weak-continuity(\mBbbB{};\mBbbB{})

Date html generated: 2020_05_20-AM-07_47_46
Last ObjectModification: 2020_01_24-PM-01_59_43

Theory : basic

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