Nuprl Lemma : qadd_preserves_qle
∀[a,b,c:ℚ]. {uiff(a ≤ b;(c + a) ≤ (c + b))}
Proof
Definitions occuring in Statement :
qle: r ≤ s,
qadd: r + s,
rationals: ℚ,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
guard: {T}
Definitions unfolded in proof :
guard: {T},
uall: ∀[x:A]. B[x],
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
implies: P ⇒ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
true: True,
squash: ↓T,
iff: P ⇐⇒ Q
Lemmas referenced :
iff_weakening_equal,
mon_ident_q,
qinverse_q,
qadd_comm_q,
qadd_ac_1_q,
true_wf,
squash_wf,
int-subtype-rationals,
qmul_wf,
grp_op_preserves_le_qorder,
rationals_wf,
qle_wf,
qadd_wf,
qle_witness
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
independent_pairFormation,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
independent_functionElimination,
productElimination,
independent_pairEquality,
isect_memberEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
independent_isectElimination,
minusEquality,
natural_numberEquality,
applyEquality,
lambdaEquality,
imageElimination,
imageMemberEquality,
baseClosed,
universeEquality
Latex:
\mforall{}[a,b,c:\mBbbQ{}]. \{uiff(a \mleq{} b;(c + a) \mleq{} (c + b))\}
Date html generated:
2016_05_15-PM-10_59_06
Last ObjectModification:
2016_01_16-PM-09_32_09
Theory : rationals
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