Nuprl Lemma : implies-quotient-true2
∀[P,Q:ℙ]. ((P ⇒ ⇃(Q)) ⇒ {⇃(P) ⇒ ⇃(Q)})
Proof
Definitions occuring in Statement :
quotient: x,y:A//B[x; y],
uall: ∀[x:A]. B[x],
prop: ℙ,
guard: {T},
implies: P ⇒ Q,
true: True
Definitions unfolded in proof :
guard: {T},
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
uimplies: b supposing a,
quotient: x,y:A//B[x; y],
and: P ∧ Q,
all: ∀x:A. B[x],
true: True
Lemmas referenced :
implies-quotient-true,
quotient_wf,
true_wf,
equiv_rel_true,
equal_wf,
equal-wf-base,
quotient-member-eq
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
lambdaFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
cumulativity,
lambdaEquality,
hypothesis,
because_Cache,
independent_isectElimination,
independent_functionElimination,
functionEquality,
universeEquality,
rename,
pointwiseFunctionalityForEquality,
pertypeElimination,
productElimination,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
productEquality,
natural_numberEquality
Latex:
\mforall{}[P,Q:\mBbbP{}]. ((P {}\mRightarrow{} \00D9(Q)) {}\mRightarrow{} \{\00D9(P) {}\mRightarrow{} \00D9(Q)\})
Date html generated:
2017_04_14-AM-07_39_57
Last ObjectModification:
2017_02_27-PM-03_11_20
Theory : quot_1
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