Nuprl Lemma : prop-truncation-quot
∀T:Type. (⇃(⇃(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
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
uall: ∀[x:A]. B[x],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
uimplies: b supposing a,
prop: ℙ,
true: True,
cand: A c∧ B,
quotient: x,y:A//B[x; y],
and: P ∧ Q,
squash: ↓T,
subtype_rel: A ⊆r B
Lemmas referenced :
prop-truncation-implies,
quotient_wf,
true_wf,
equiv_rel_true,
equal-wf-base,
equal_wf,
squash_wf,
quotient-member-eq
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isectElimination,
because_Cache,
sqequalRule,
lambdaEquality,
hypothesis,
independent_isectElimination,
independent_functionElimination,
cumulativity,
hypothesisEquality,
universeEquality,
promote_hyp,
natural_numberEquality,
independent_pairFormation,
pointwiseFunctionality,
pertypeElimination,
productElimination,
productEquality,
applyEquality,
imageElimination,
equalityTransitivity,
equalitySymmetry,
imageMemberEquality,
baseClosed
Latex:
\mforall{}T:Type. (\00D9(\00D9(T)) {}\mRightarrow{} \00D9(T))
Date html generated:
2017_04_17-AM-09_57_39
Last ObjectModification:
2017_02_27-PM-05_50_51
Theory : continuity
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