Nuprl Lemma : prop-truncation-implies
∀T:Type. ((∀a,b:T. (a = b ∈ T)) ⇒ ⇃(T) ⇒ T)
Proof
Definitions occuring in Statement :
quotient: x,y:A//B[x; y],
all: ∀x:A. B[x],
implies: P ⇒ Q,
true: True,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
so_apply: x[s],
so_lambda: λ2x.t[x],
uimplies: b supposing a,
so_apply: x[s1;s2],
so_lambda: λ2x y.t[x; y],
prop: ℙ,
uall: ∀[x:A]. B[x],
guard: {T},
label: ...$L... t,
and: P ∧ Q,
quotient: x,y:A//B[x; y],
member: t ∈ T,
implies: P ⇒ Q,
all: ∀x:A. B[x]
Lemmas referenced :
equal_wf,
all_wf,
equiv_rel_true,
quotient_wf,
true_wf,
equal-wf-base
Rules used in proof :
universeEquality,
independent_isectElimination,
lambdaEquality,
cumulativity,
because_Cache,
isectElimination,
extract_by_obid,
productEquality,
equalitySymmetry,
equalityTransitivity,
dependent_functionElimination,
hypothesis,
thin,
productElimination,
cut,
pertypeElimination,
sqequalRule,
sqequalHypSubstitution,
hypothesisEquality,
pointwiseFunctionalityForEquality,
introduction,
rename,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}T:Type. ((\mforall{}a,b:T. (a = b)) {}\mRightarrow{} \00D9(T) {}\mRightarrow{} T)
Date html generated:
2017_09_29-PM-06_07_26
Last ObjectModification:
2017_09_04-PM-03_51_03
Theory : continuity
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