Nuprl Lemma : qadd_preserves_eq
∀[a,b,c:ℚ]. uiff(a = b ∈ ℚ;(c + a) = (c + b) ∈ ℚ)
Proof
Definitions occuring in Statement :
qadd: r + s,
rationals: ℚ,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
prop: ℙ,
subtype_rel: A ⊆r B,
true: True,
squash: ↓T,
guard: {T},
iff: P ⇐⇒ Q,
implies: P ⇒ Q
Lemmas referenced :
and_wf,
equal_wf,
rationals_wf,
qadd_wf,
qmul_wf,
int-subtype-rationals,
squash_wf,
true_wf,
qadd_ac_1_q,
qadd_comm_q,
qinverse_q,
mon_ident_q,
iff_weakening_equal
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
independent_pairFormation,
equalitySymmetry,
dependent_set_memberEquality,
hypothesis,
hypothesisEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
applyLambdaEquality,
setElimination,
rename,
productElimination,
sqequalRule,
independent_pairEquality,
isect_memberEquality,
axiomEquality,
because_Cache,
equalityTransitivity,
minusEquality,
natural_numberEquality,
applyEquality,
lambdaEquality,
imageElimination,
universeEquality,
imageMemberEquality,
baseClosed,
independent_isectElimination,
independent_functionElimination
Latex:
\mforall{}[a,b,c:\mBbbQ{}]. uiff(a = b;(c + a) = (c + b))
Date html generated:
2018_05_21-PM-11_56_13
Last ObjectModification:
2017_07_26-PM-06_46_46
Theory : rationals
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